Gröbner Basis, Integration and Transcendental Functions. - Nobuki Takayama (ISSAC, 1990)

An Algorithm of Constructing the Integral of a Module - an Infinite Dimensional Analog of Gröbner Basis. - Nobuki Takayama (ISSAC, 1990)

An Approach to the Zero Recognition Problem by Buchberger Algorithm. - Nobuki Takayama (J. Symb. Comput., 1992)

An Algorithm for Finding Recurrence Ralations of Binomial Sums and its Complexity. - Nobuki Takayama (J. Symb. Comput., 1995)

A Localization Algorithm for D-modules. - Toshinori Oaku; Nobuki Takayama; Uli Walther (J. Symb. Comput., 2000)

Minimal Free Resolutions of Homogenized D-modules. - Toshinori Oaku; Nobuki Takayama (J. Symb. Comput., 2001)

Generating Kummer Type Formulas for Hypergeometric Functions. - Nobuki Takayama (Algebra, Geometry, and Software Systems, 2003)

Editorial. - Arjeh M. Cohen; Xiao-Shan Gao; Nobuki Takayama (J. Symb. Comput., 2004)

Tangent cone algorithm for homogenized differential operators. - Michel Granger; Toshinori Oaku; Nobuki Takayama (J. Symb. Comput., 2005)

Links to Projects. Mathematical Software, icms2006 - Developer's Meeting. - Masayuki Noro; Nobuki Takayama (ICMS, 2006)

Solutions of polynomial systems derived from the steady cavity flow problem. - Martin Mevissen; Kosuke Yokoyama; Nobuki Takayama (ISSAC, 2009)

Computing Differential Equations for Integrals Associated to Smooth Fano Polytopes - Hiromasa Nakayama; Nobuki Takayama (CoRR, 2010)

Holonomic gradient descent and its application to the Fisher-Bingham integral. - Hiromasa Nakayama; Kenta Nishiyama; Masayuki Noro; Katsuyoshi Ohara; Tomonari Sei; Nobuki Takayama; Akimichi Takemura (Adv. Appl. Math., 2011)

Pfaffian Systems of A-Hypergeometric Equations - Takayuki Hibi; Kenta Nishiyama; Nobuki Takayama (CoRR, 2012)

The holonomic gradient method for the distribution function of the largest root of a Wishart matrix. - Hiroki Hashiguchi; Yasuhide Numata; Nobuki Takayama; Akimichi Takemura (J. Multivar. Anal., 2013)

Properties and applications of Fisher distribution on the rotation group. - Tomonari Sei; Hiroki Shibata; Akimichi Takemura; Katsuyoshi Ohara; Nobuki Takayama (J. Multivar. Anal., 2013)

Software Packages for Holonomic Gradient Method. - Tamio Koyama; Hiromasa Nakayama; Katsuyoshi Ohara; Tomonari Sei; Nobuki Takayama (ICMS, 2014)

Computing Bases of Twisted Cohomology Groups for Sparse Polynomials. - Takayuki Hibi; Kenta Nishiyama; Nobuki Takayama (ACM Commun. Comput. Algebra, 2014)

Holonomic gradient descent for the Fisher-Bingham distribution on the (d)-dimensional sphere. - Tamio Koyama; Hiromasa Nakayama; Kenta Nishiyama; Nobuki Takayama (Comput. Stat., 2014)

Pfaffian Systems of A-Hypergeometric Systems II - Holonomic Gradient Method. - Katsuyoshi Ohara; Nobuki Takayama (CoRR, 2015)

A-hypergeometric distributions and Newton polytopes. - Nobuki Takayama; Satoshi Kuriki; Akimichi Takemura (Adv. Appl. Math., 2018)

Distribution of the ratio of two Wishart matrices and cumulative probability evaluation by the holonomic gradient method. - Hiroki Hashiguchi; Nobuki Takayama; Akimichi Takemura (J. Multivar. Anal., 2018)

Computations of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Wishart Matrix. - Nobuki Takayama; Lin Jiu; Satoshi Kuriki; Yi Zhang (CoRR, 2019)

Algorithms for Pfaffian Systems and Cohomology Intersection Numbers of Hypergeometric Integrals. - Saiei-Jaeyeong Matsubara-Heo; Nobuki Takayama (ICMS, 2020)

Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix. - Nobuki Takayama; Lin Jiu; Satoshi Kuriki; Yi Zhang 088 (J. Multivar. Anal., 2020)

Fast evaluation of some p-adic transcendental functions. - Xavier Caruso; Marc Mezzarobba; Nobuki Takayama; Tristan Vaccon (CoRR, 2021)

Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics. - Nobuki Takayama; Takaharu Yaguchi; Yi Zhang (CoRR, 2021)

An Application of the Holonomic Gradient Method to the Neural Tangent Kernel. - Akihiro Sakoda; Nobuki Takayama (CoRR, 2024)